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Dynamic Bayesian networks have been well explored in the literature as discrete-time models: however, their continuous-time extensions have seen comparatively little attention. In this paper, we propose the first constraint-based algorithm…
Rating systems play an important role in competitive sports and games. They provide a measure of player skill, which incentivizes competitive performances and enables balanced match-ups. In this paper, we present a novel Bayesian rating…
Causal Bayesian networks (CBN) are popular graphical probabilistic models that encode causal relations among variables. Learning their graphical structure from observational data has received a lot of attention in the literature. When there…
Mechanism design is essentially reverse engineering of games and involves inducing a game among strategic agents in a way that the induced game satisfies a set of desired properties in an equilibrium of the game. Desirable properties for a…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
We study the problem of learning the best Bayesian network structure with respect to a decomposable score such as BDe, BIC or AIC. This problem is known to be NP-hard, which means that solving it becomes quickly infeasible as the number of…
Human networks greatly impact important societal outcomes, including wealth and health inequality, poverty, and bullying. As such, understanding human networks is critical to learning how to promote favorable societal outcomes. As a step…
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…
Game theory is appropriate for studying cyber conflict because it allows for an intelligent and goal-driven adversary. Applications of game theory have led to a number of results regarding optimal attack and defense strategies. However, the…
This paper presents an in-depth statistical analysis of an experiment designed to measure the extent to which players in a simple game behave according to a popular behavioral economic model. The p-beauty contest is a multi-player number…
Learning Bayesian networks is often cast as an optimization problem, where the computational task is to find a structure that maximizes a statistically motivated score. By and large, existing learning tools address this optimization problem…
Modeling the interaction between traffic agents is a key issue in designing safe and non-conservative maneuvers in autonomous driving. This problem can be challenging when multi-modality and behavioral uncertainties are engaged. Existing…
In two-player cooperative games, agents can play together effectively when they have accurate assumptions about how their teammate will behave, but may perform poorly when these assumptions are inaccurate. In language games, failure may be…
We showcase in this paper the use of some tools from network theory to describe the strategy of football teams. Using passing data made available by FIFA during the 2010 World Cup, we construct for each team a weighted and directed network…
Among the most fundamental tools for social network analysis are centrality measures, which quantify the importance of every node in the network. This centrality analysis typically disregards the possibility that the network may have been…
Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches…
Learning the structure of Bayesian networks from data is known to be a computationally challenging, NP-hard problem. The literature has long investigated how to perform structure learning from data containing large numbers of variables,…
We investigate the accuracy of prediction in deterministic learning dynamics of zero-sum games with random initializations, specifically focusing on observer uncertainty and its relationship to the evolution of covariances. Zero-sum games…
The Stackelberg game depicts a leader-follower relationship wherein decisions are made sequentially, and the Stackelberg equilibrium represents an expected optimal solution when the leader can anticipate the rational response of the…
Cybersecurity risk analysis plays an essential role in supporting organizations make effective decision about how to manage and control cybersecurity risk. Cybersecurity risk is a function of the interplay between the defender, i.e., the…